Learn Hardcore Greek: Όταν έρθεις από το ταξίδι, θα έχω ήδη διαβάσει το μήνυμά σου. - When you come back from the trip, I will already have read your message.

Όταν έρθεις = when you (will) come / when you come (in the future, one specific time).
Όταν έρχεσαι = when you come (whenever you come, in general / habitually).

So:

Όταν έρθεις από το ταξίδι… = one specific future arrival, after this trip.
Όταν έρχεσαι από το ταξίδι, είσαι κουρασμένος. = every time you come back from a trip, you are tired (habitual).

That’s why έρθεις is used here.

Is έρθεις a future tense? How is it different from θα έρθεις?

έρθεις by itself is not a future tense. It is the aorist subjunctive, 2nd person singular.

θα έρθεις = future indicative: you will come.
(όταν) έρθεις = aorist subjunctive: when you come (used in time clauses about the future).

Greek does not say:

✗ Όταν θα έρθεις …

Instead, you use όταν + subjunctive:

✓ Όταν έρθεις … (when you come)
✓ Όταν φύγεις … (when you leave)
✓ Όταν το δεις … (when you see it)

Why is θα έχω ήδη διαβάσει used instead of just θα διαβάσω?

Θα έχω ήδη διαβάσει is the future perfect, similar to English “will have (already) read”. It focuses on:

an action completed before a specific future moment.

Here, the future moment is όταν έρθεις από το ταξίδι (when you come back from the trip).
So:

Θα έχω ήδη διαβάσει το μήνυμά σου.
= By the time you get back, the reading will already be finished.

If you said:

Θα διαβάσω το μήνυμά σου.
= I will read your message (sometime in the future – no clear relation to your return).

Both are grammatically correct, but the original sentence specifically expresses “already finished by then”, which is why the future perfect is used.

How is θα έχω ήδη διαβάσει formed? What are its parts?

The structure is very close to English:

θα – the future particle.
έχω – present tense of έχω (I have).
διαβάσει – the “have‑read” form of διαβάζω (the perfect/aorist stem used with έχω).

So:

έχω διαβάσει = I have read (present perfect).
θα έχω διαβάσει = I will have read (future perfect).
θα έχω ήδη διαβάσει = I will already have read.

Just remember: future perfect = θα + έχω (conjugated) + perfect form of the main verb.

Why is ήδη placed between έχω and διαβάσει? Could it go somewhere else?

Placing ήδη between the auxiliary and the main verb is very natural:

Θα έχω ήδη διαβάσει το μήνυμά σου.

You also have a few other acceptable positions, with slightly different emphasis:

Ήδη θα έχω διαβάσει το μήνυμά σου. (stronger emphasis on already.)
Θα έχω διαβάσει ήδη το μήνυμά σου.

All of these are grammatically correct.
A good default pattern is:

θα + έχω + ήδη + [perfect form of verb]

Why is there a comma between Όταν έρθεις από το ταξίδι and θα έχω ήδη διαβάσει το μήνυμά σου?

Όταν έρθεις από το ταξίδι is a subordinate time clause placed at the beginning of the sentence. In Greek, when such a clause comes first, it is normally followed by a comma:

Όταν τελειώσω, θα σε πάρω τηλέφωνο.
Αν βρέξει, δεν θα πάμε.

If the main clause comes first, the comma is often omitted unless needed for clarity:

Θα σε πάρω τηλέφωνο όταν τελειώσω. (usually no comma)

What exactly does από το ταξίδι mean here? Why από?

Από is a very common preposition meaning from (among other things).
In this sentence:

από το ταξίδι = from the trip → back from the trip.

So Όταν έρθεις από το ταξίδι literally is “when you come from the trip”, which in natural English is “when you come back from the trip”.

από here shows origin / point of return:

Έρχομαι από τη δουλειά. = I’m coming from work.
Γύρισα από τις διακοπές. = I came back from vacation.

You could say things like:

Όταν γυρίσεις από το ταξίδι… = when you return from the trip… (more explicitly “return”).

But έρθεις από το ταξίδι is perfectly normal and understood as “come back from the trip”.

Why is it το ταξίδι and not some other case? What case is used after από?

Το ταξίδι is in the accusative case.

In Modern Greek, από is normally followed by the accusative:

από το σπίτι
από τη δουλειά
από το ταξίδι

So the pattern is:

από + accusative = from X.

Here, το ταξίδι is just the regular neuter accusative singular form of το ταξίδι.

Why is it written το μήνυμά σου and not το μήνυμα σου?

The difference is the position of the stress.

Alone: το μήνυμα – stress on the first syllable (μή).
With the enclitic σου: το μήνυμά σου – stress moves to the last syllable of μήνυμα.

When a word stressed on the third syllable from the end (like μήνυμα) is followed by an unstressed short word such as μου, σου, του, etc., the stress shifts one syllable to the right to keep the overall stress pattern of Greek.

So you must write:

το μήνυμα (no σου)
το μήνυμά σου (with σου)

The accent mark on -μά is obligatory; το μήνυμα σου would be considered orthographically wrong.

Why does σου come after μήνυμά? Can I say το σου μήνυμα like in English “your message”?

No: in Greek, the weak possessive pronouns (μου, σου, του, της, μας, σας, τους) normally come after the noun:

το μήνυμά σου = your message
ο φίλος μου = my friend
το βιβλίο της = her book

So the natural order is:

article + noun (+ its accent shift, if needed) + weak possessive pronoun

If you want to emphasize your, you don’t move σου in front; instead you use δικός/δική/δικό:

το δικό σου μήνυμα = your message (as opposed to someone else’s).

But the basic, unmarked form is το μήνυμά σου, not το σου μήνυμα.

What is the function of σου here exactly? Is it like “you” or “your”?

Σου here is a weak (clitic) possessive pronoun meaning “your”.

εσύ = you (subject pronoun).
σου = your / (to) you, depending on context.

In this sentence:

το μήνυμά σου = your message.

Same usage:

ο αδερφός σου = your brother
η τσάντα σου = your bag

So σου does not mean “you” as a subject; it shows possession.

Could I also say Θα έχω ήδη διαβάσει το μήνυμά σου όταν έρθεις από το ταξίδι? Is there any difference?

Yes, that word order is also correct:

Θα έχω ήδη διαβάσει το μήνυμά σου όταν έρθεις από το ταξίδι.

The meaning is essentially the same. The difference is just what comes first:

Όταν έρθεις από το ταξίδι, θα έχω ήδη διαβάσει το μήνυμά σου.
– Slight emphasis on the time condition (“when you come back…”).
Θα έχω ήδη διαβάσει το μήνυμά σου όταν έρθεις από το ταξίδι.
– Slight emphasis on what I will have done.

Both are natural; choosing one or the other is mostly stylistic.

Could I use αν instead of όταν here? What would change?

You can use αν, but it changes the meaning:

Όταν έρθεις από το ταξίδι… = when you come back from the trip (it is taken for granted that you will).
Αν έρθεις από το ταξίδι… = if you come back from the trip (it sounds like there is some doubt about whether you will come).

In your context, we normally expect the person to come back, so όταν (“when”) is the natural choice. Use αν for real conditions (“if”), not for certain future events.